Second-order metropolitan urban phase transitions

The morphology evolution of Metropolitan Urban Areas constituted by different Central Business Districts is studied in this paper. For this matter, we propose a stochastic model which combines an initial percolation setting followed by a diffusion-limited aggregation mechanism. Our model mimics better than either case (percolation or diffusion-limited aggregation) the Metropolitan Urban Areas formation progress. We argue that the Metropolitan Urban Areas case introduced in this paper, grows in such a way that undergoes a non-equilibrium second-order phase transition during this process. This conclusion is supported by a fractal dimension and configurational entropy analysis, as well as by studying an empirical case.